{
  "id": "0807.2233",
  "version": "v4",
  "published": "2008-07-14T19:40:57.000Z",
  "updated": "2015-02-25T14:58:48.000Z",
  "title": "Aspects of area formulas by way of Luzin, Radó, and Reichelderfer on metric measure spaces",
  "authors": [
    "Niko Marola",
    "William P. Ziemer"
  ],
  "journal": "J. Math. Soc. Japan 67 (2015), 561-579",
  "categories": [
    "math.CA",
    "math.MG"
  ],
  "abstract": "We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit a Poincar\\'e inequality and are equipped with a doubling measure. The properties we have selected to study are those that are related to area formulas.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2011-03-11T09:11:26.000Z",
      "title": "Sobolev-type functions on metric spaces: area and co-area formulas by way of Luzin, Rado, and Reichelderfer",
      "abstract": "We consider some measure-theoretic properties of functions belonging to a Sobolev-type class on metric measure spaces that admit both a Poincar\\'e inequality and are equipped with a doubling measure. The properties we have selected to study are those that are closely related to area and coarea formulas. We present these formulas for Newton-Sobolev functions in the abstract metric setting.",
      "comment": null,
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-02-25T14:58:48.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46E35",
      "46E40",
      "30L99",
      "28A99"
    ],
    "keywords": [
      "metric spaces",
      "co-area formulas",
      "sobolev-type functions",
      "reichelderfer",
      "metric measure spaces"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0807.2233M"
    }
  }
}